From 841e596ad02b1b99e6c9578e9ecc5b0b56277948 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Mon, 3 Jul 2023 11:39:38 +0000
Subject: [PATCH] Final clean-up of the idea of using Dekker double-precision
 floating computations to improve accuracy.

FossilOrigin-Name: 40285d631072b79aba39cc20d4b217bdf0069f29ac9902cb97dec28d3e4cde11
---
 manifest      | 12 ++++++------
 manifest.uuid |  2 +-
 src/util.c    | 15 ++++++++++++---
 3 files changed, 19 insertions(+), 10 deletions(-)

diff --git a/manifest b/manifest
index b7a2f9af88..7130835d4e 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Squeeze\sas\smany\sbits\sas\swe\scan\sout\sof\snormalization.
-D 2023-07-03T10:35:29.478
+C Final\sclean-up\sof\sthe\sidea\sof\susing\sDekker\sdouble-precision\sfloating\ncomputations\sto\simprove\saccuracy.
+D 2023-07-03T11:39:38.542
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c 78be1d552e7038265bb944ef26c9ef94514bd061da19323a0321dde2874f0907
+F src/util.c 44855f67ac96b546b77b6c2ad128d1e28a56c495038cdda3cae25b8407442f3c
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -2041,8 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P 2994caf5884be07c889519c78fbac4ddcf267fcfe6a3265ecb6390bcd574532e
-R 50ea777199102a639989a65cb4bb5a5a
+P 25d1ad6df1ed460c2cc9f32e8a5106e121ae502044f83abf431c1d5b3879eb56
+R 8a559af6860b1623fc9d9f5fb9393b11
 U drh
-Z 91cee9d1957f1c63a4a3d422340e91a7
+Z 48672189b786297b4026c7966b4eccaa
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index a5a0d7abae..7757e469cd 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-25d1ad6df1ed460c2cc9f32e8a5106e121ae502044f83abf431c1d5b3879eb56
\ No newline at end of file
+40285d631072b79aba39cc20d4b217bdf0069f29ac9902cb97dec28d3e4cde11
\ No newline at end of file
diff --git a/src/util.c b/src/util.c
index 6e740ef6ae..cf4745bd0b 100644
--- a/src/util.c
+++ b/src/util.c
@@ -999,8 +999,8 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
   /* Multiply r by powers of ten until it lands somewhere in between
   ** 1.0e+19 and 1.0e+17.
   */
-  if( sizeof(long double)>8 && 0 ){
-    long double rr = r;
+  if( sizeof(LONGDOUBLE_TYPE)>8 ){
+    LONGDOUBLE_TYPE rr = r;
     if( rr>=1.0e+19 ){
       while( rr>=1.0e+119L ){ exp+=100; rr *= 1.0e-100L; }
       while( rr>=1.0e+29L  ){ exp+=10;  rr *= 1.0e-10L;  }
@@ -1012,6 +1012,15 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
     }
     v = (u64)rr;
   }else{
+    /* If high-precision floating point is not available using "long double",
+    ** then use Dekker-style double-double computation to increase the
+    ** precision.
+    **
+    ** The error terms on constants like 1.0e+100 computed using the
+    ** decimal extension, for example as follows:
+    **
+    **   SELECT decimal_sci(decimal_sub('1.0e+100',decimal(1.0e+100)));
+    */
     double rr = 0.0;
     if( r>1.84e+19 ){
       while( r>1.84e+119 ){
@@ -1029,7 +1038,7 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
     }else{
       while( r<1.84e-82  ){
         exp -= 100;
-        mul2(r, rr, 1.0e+100, -1.5902891109759918046, &r, &rr);
+        mul2(r, rr, 1.0e+100, -1.5902891109759918046e+83, &r, &rr);
       }
       while( r<1.84e+08  ){
         exp -= 10;